A175618 Decimal expansion of product_{n>=2} (1-n^(-7)).

9, 9, 1, 6, 5, 4, 9, 5, 3, 4, 7, 2, 8, 3, 4, 4, 5, 7, 4, 0, 1, 3, 2, 3, 3, 7, 0, 5, 6, 9, 0, 2, 7, 4, 2, 5, 8, 6, 4, 2, 6, 8, 0, 8, 3, 5, 4, 1, 0, 3, 8, 5, 0, 3, 4, 9, 7, 6, 6, 3, 4, 9, 2, 1, 4, 1, 7, 0, 5, 1, 4, 3, 6, 3, 2, 8, 4, 3, 1, 9, 7, 1, 1, 8, 0, 2, 3, 9, 5, 0, 3, 8, 3, 0, 4, 3, 7, 9, 5, 5, 2, 1, 1, 9, 5

Offset

0,1

Links

Table of n, a(n) for n=0..104.

E. Weisstein, Infinite Product, Mathworld.

Formula

Equals 1/product_{t=1..6} Gamma(2-exp(2*Pi*i*t/7)), where i is the imaginary unit and 2*Pi/7 = A019695.

Equals exp(Sum_{j>=1} (1 - zeta(7*j))/j). - Vaclav Kotesovec, Dec 15 2020

Example

0.99165495...

Mathematica

N[1/(7*Product[ Gamma[(-1)^(8*k/7 + 1)], {k, 1, 6}]), 105] // Re // RealDigits // First (* Jean-François Alcover, Feb 05 2013 *)

Prog

(PARI) exp(suminf(j=1, (1 - zeta(7*j))/j)) \\ Vaclav Kotesovec, Dec 15 2020

Crossrefs

Cf. A109219, A175615, A144666.

Sequence in context: A144982 A228788 A019788 * A346439 A266555 A343367

Adjacent sequences: A175615 A175616 A175617 * A175619 A175620 A175621

Keyword

cons,easy,nonn

Author

R. J. Mathar, Jul 26 2010

Status

approved